Cosmic topology can be described as the effort to determine the shape of our universe through observational techniques. In this chapter we discuss two programs of research in cosmic topology: the cosmic crystallography method and the circles-in-the-sky method. Both programs search for topology by assuming the universe is finite in volume without boundary. The chapter begins with a discussion of three-dimensional geometry and some 3-manifolds that have been given consideration as models for the shape of our universe.
